Business Maths 25 Sept

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BUSINESS MATHEMATICS AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

BUSINESS MATHEMATICS Dr. T.K. Jain.

AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk, www.afterschoool.tk www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

A train 180 m long crosses a signal post in 9 seconds. The time taken by the train to cross a bridge 270 m long is • The speed of the train is 180 / 9 = 20 meters per second. • Distance to cover: 180+270 =450 meters • =450 / 20 = 22.5 seconds. Answer

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

If the equation X^2 +2 (K-4)X +4 =0 has equal roots, what is the value of K? • • • •

B^2 = 4ac (The essential condition) k^2 - 8k+12 =0; K^2-6k+2K +12 =0 K = 6 and K = 2 answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

If there are two concentric circles on a plane such that the area of the inner circle is one-fourth the area of the outer circle, then the ratio of the circumference of the outer to the inner circle is • we know that the formula of circles is pi*r^2. Thus the area is always squared. But circumference is not squared (2pi*r). • Let us take a hypothetical example. . . www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Solution . . • Let us assume that areas of two circles are 154 and 616 (their radius are 7 and 14 respectively. Thus their circumference is in the ratio of 1:2. as you can see: their circumferences are 44 and 88. • Answer = 1:2 answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

A tank is attached with three taps A, B and C such that the inlet taps A and B can fill the tank completely • in 20 and 30 minutes respectively and the outlet tap C can empty the completely filled tank in 25 minutes. If all the taps are opened simultaneously, then in what time will the tank be full? (Consider the tank is empty at the beginning.) www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Solution . . • 1/20 +1/30 – 1/25 • We take LCM of 20, 25 and 30. The LCM is 2*2*5*5*3 = 300 • We get (15+10-12)/300 = 13/300. • Now we reverse it : 300/13 = 23 minutes approximately. Answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

The area of a square is 324 sq.cm. If a circle has a diameter which is of the same length as the side of the square, the area of the circle would be • One side of square is square root of 324 or 18. • Radius of the circle is half of diameter (18) = 9. thus the area of the circle is Pi*r*r • =22/7*9*9 = 254.57 answer. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Sudha and Nidhi can do a piece of work in 20 days. Nidhi alone can do it in 30 days. In how many days can Sudha alone do it? • 1/20 – 1/30 • =(3-2)/60 = 1/60 • Or in 60 days. (Sudha alone can do the work in 60 days.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

In a right-angled triangle, the length of the hypotenuse is 22 cm and one of the angles is 30°. What is the length of the side opposite to this angle? • We know that Sin 30 is ½. Thus Per/Hyp. =½ • Thus Per / 22 = ½ or Per = 11answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

The area of a square field is 24,200 sq.m. How long will a person take to cross the field diagonally at the rate of 6.6 km/hr? • One side of square = square root of 24200. = 155.56 • The diagonal of the field = 1.41*155.56 = 220 • The time taken will be 220/6600 *60= 2 minutes. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

A spherical pear of radius 4 cm is to be divided into eight identical parts by cutting it vertically four times. What is the surface area of each of the final piece? • the total surface area of the pear is 2*pi*r*r = 2*22/7*4*4 =100.57 now divide it by 8 = 12.57 • We have to add inner plain area also in this. This is pi*r*r = 22/7*4*4 = 50.28 Now add these two, we get 62.8 CM answer. www.afterschoool.tk AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

If the diagonal and the area of a rectangle are 25 m and 168 m respectively, what is the length of the rectangle? • • • •

Area = L *B = 168 Diagonal = sqrt(L^2 +B^2) = 25 If we look at the factors of 168, we find: =2*2*2*3*7 so let us try with 24*7 as an option. The squares of 24 and 7 are 576 +49, the squreroot of which is 25. Answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Manjari had to do a multiplication. Instead of taking 53, she took 35 as one or the mulupliers. As a result, the product was 540 less than what it would have originally been. What is the value obtained by Manjari after multiplication? • (X*53) – (X*35) = 540 • =18X = 540 OR X = 30. Manjari got (30*35) = 1050 as the outcome. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

In how many ways, 4 boys and 7 girls can be arranged in a row so that all the boys are together? • Let us assume these 4 boys as one unit. Thus we have 8 units now (7+1) whom we can place in a row and find the number of possibilities. The total number of possibilities are : 8*7*6*5*4*3*2*1=40320 answer. www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

If a tap fills (1/4)th of a bucket in 3 minutes, in how many minutes will it fill (5/8)th of the bucket? • It takes 3 minutes to fill 2/8 and we know that 2.5 time of 2 is 5. Thus 5/8 will be filled in 2.5*3 = 7.5 minutes answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Three circles, with centers A, B and C having radii of 6 cm, 7 cm and 8 cm respectively, touch each other externally. What is the area of the triangle formed by joining the centers of these circles? • One side of the triangle is (6+7) =13, the other sides are (7+8) = 15 and (6+8) = 14. Now let us find S = (13+14+15)/2 = 21 • Area =sqrt(21*8*7*6) = 84 answer www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

A tree doubles its height in one week. If After 12 weeks, its height is 12 feet; when was its height 6 feet? • 11 weeks. Answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

The weight of one brick is equal to ¾ KG + ¾ Brick. What is the weight of the brick? • 1/4th of the brick is equal to ¾ KG. • Thus the weight of the brick is 4*3/4 KG • =3 KG answer.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

ABOUT AFTERSCHO☺OL Afterschoool conducts three year integrated PGPSE (after class 12th along with IAS / CA / CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Why such a programme? • To promote people to take up entrepreneurship and help develop the society • To enable people to take up franchising and other such options to start a business / social development project • To enable people to take up social development as their mission • To enable people to promote spirituality and positive thinking in the world www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Who are our supporters? • Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. • You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs • • • • •

Most flexible, adaptive but rigorous programme Available in distance learning mode Case study focused- latest cases Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn • The only absolutely free course on internet www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Workshops from AFTERSCHO☺OL • • • • • • • • •

IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Flexible Specialisations: • • • • • • • • • •

Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who want to achieve success in life – not just a degree • Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested • Admissions open throughout the year • Latest and most advanced technologies, books and study material www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Components • • • • • • • • • • • • • •

Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Pedagogy • • • • • • • • •

Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment Mentoring and counselling Study exchange programme (with institutions out of India) • Rural development / Social welfare projects www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Branches • AFTERSCHO☺OL will shortly open its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Case Studies • We want to write case studies on social entrepreneurs, first generation entrepreneurs, ethical entrepreneurs. Please help us in this process. Help us to be in touch with entrepreneurs, so that we may develop entrepreneurs.

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

Basic values at AFTERSCHO☺OL • • • • • •

Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support and help • Ask fundamental questions : why, when, how & where? • Embrace change – and compete with yourself only www.afterschoool.tk

AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

www.afterschoool.tk social entrepreneurship for better society

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AFTERSCHO☺OL's MATERIAL FOR PGPSE PARTICIPANTS

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